Question

Fluidyne Corporation manufactures and sells water filters. The economic forecasting unit of the company has supplied the following demand equation:   

QB=    2000 -     5PB +   2.5PC   +   0.82Y   + 0.6AB

          (1200)       (1.5)       (1.2)            (0.5)      (0.2)

Where,

QB=quantity sold

PB=price per unit

PC=average unit price of competitor’s product

Y=income per household

AB=advertising expenditure

           

            R2= 0.86

S.E.E=5

Standard error of coefficients in parentheses (1200) (1.5) (1.2,) (0.5) , ( 0.2)

Given, PB=$50,    PC=$45,      AB=$12,500      Y=$2,000

1. Does each independent variable have a significant effect on the sales of Fluidyne water filters?
2. Interpret the coefficient of variables that are significant?
3. Interpret the coefficient of determination(R²)
4. Determine the monthly quantity demanded sold (QB) for water filter?
5. Is the quantity demanded for water filter (QB) sensitive to its own price?
6. Is water filter a luxury or necessity?

Answer 1

a) To test this, we need to calculate the t statistic for each of the variables and compare them to the critical value based on the level of significance.

T stat = coefficient/standar error

PB = -5/1.5 = 3.33

PC = 2.5/1.2 = 2.08

Y = 0.82/0.5 = 1.64

AB = 0.6/0.2 = 3

At the significance level of 5%, Y is not significant as its t stat is less than the critical value (1.96).

b) Price per unit has an inverse relationship with quantity sold (i.e. higher the price, lesser the quantity sold), average price of competitor's product and advertising expenditure have positive relationship with quantity sold (i.e. higher the competitor's price or advertising, greater the units sold)

c) The coefficient of determination signifies the goodness of fit of the regression equation. A value of 0.86 signifies a good fit and estimation.

d) Monthly quantity demanded =  2000-5*50+2.5*45+0.6*12500 = 9362.5

e) Yes, the coefficient is significant and negative

f) elasticity = dy/dx * x/y

here dy/dx represents the coefficient of PB where Y is QB and X is PB

elasticity = -5*50/9362.5 = -0.0267, since |elasticity|<1, this is a necessity